Method and apparatus for measuring signal pulse energy

ABSTRACT

The energy E of a signal pulse P inputted to an energy measurement apparatus  1  for measurement, and corresponding to the total integrated intensity, is calculated in an energy calculation unit  10  from the integrated signal intensity Q acquired by a gate integrator  32,  and from the pulse interval T measured by a pulse interval measurement unit  23.  At this time, pileup correction is performed using at least one of the integrated signal intensity or the energy, and the pulse interval of the signal pulse inputted prior to the signal pulse for measurement. By this means, the correct energy E, with the effect of pileup eliminated, can be determined with good precision. Hence a method and apparatus for energy measurement are realized which enable correct and precise measurement of the energy of individual signal pulses, even when the pulse interval between signal pulses is short.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] This invention relates to a method and apparatus for measuringthe energy of a signal pulse, by integrating the signal intensity of thepulse waveform of the input signal pulse. This invention is widely usednot only in measurements of the energy of radiation and in dosimetry,but in measurement of radiation detection positions, radiation imagesand other areas, and in particular is applied in gamma cameras used innuclear medical diagnostics, in SPECT (Single Photon Emission ComputedTomography) systems, and in PET (Positron Emission Tomography) systems.

[0003] 2. Description of the Related Art

[0004] When performing measurements of γ rays, charged particle beamsand other radiation (energy beams), a scintillation detector using ascintillator, or some other radiation detector is used. The detectionsignal output from the radiation detector is subjected to prescribedsignal processing or to other processing to obtain the requiredinformation.

[0005] For example, using a scintillation detector, radiation incidenton the scintillator is detected through the scintillation light pulsesoccurring in the scintillator. Optical signal pulses resulting from thisscintillation light are converted into electrical signal pulses by aphotomultiplier tube or other photodetector. That is, when thescintillation light is incident on the photoelectric surface of aphotomultiplier tube, a plurality of photoelectrons are generated fromthe photoelectric surface, in proportion to the light intensity; afterthese photoelectrons are collected by a first dynode, the electricalsignal is amplified by successive dynodes in sequence, and output as apulse signal (electrical current signal).

[0006] In general, the scintillation light of a scintillator used in aradiation detector has a pulse waveform, with the signal intensity beingattenuated exponentially, for example. The total number ofphotoelectrons collected by the first dynode corresponds to the energyof the radiation absorbed by the scintillator. Hence in order to measurethe energy of the radiation, the output signal from a photomultipliertube must be integrated over an appropriate time interval. In general,the total number of photoelectrons collected by the first dynode as aresult of one signal pulse is not sufficiently large, and so it ispreferable that the above integration time be set so as to integratemost of the scintillation light. If the integration time is short, thenumber of photoelectrons collected is decreased, and so the energyresolution is degraded due to statistical fluctuations.

[0007] If measurements are performed in a state in which the number ofdetections (count rate) of radiation per unit time by the radiationdetector is high, then the probability is increased that the pulseinterval between signal pulses will be approximately the same as, orshorter than, the pulse width of individual pulses, so that so-called“pileups” in which two or more signal pulses overlap temporally occur.At such times, if the signal intensity (current signal) of a signalpulse the energy of which is to be measured is integrated, the signalintensity of another signal pulse with which the signal pulse haspiled-up is simultaneously integrated, and so there arises the problemthat the energy of the signal pulse being measured cannot be accuratelymeasured.

[0008] When a pulse waveform is represented by a single exponentialfunction, a comparatively simple method which is conventionally used toreduce the error due to pileups involves shortening the time width ofpulses using the delay line clipping method, and setting the integrationtime to be approximately equal to the pulse time width. In this case,the shorter the pulse time width is made, the more the integration timecan be shortened, so that the probability of occurrence of pileups isdecreased at high count rates, and the count rate characteristic can beimproved. On the other hand, the number of photoelectrons collected atthe first dynode of the photomultiplier tube for each signal pulse isreduced, and so there is the drawback that even at low count rates atwhich pileups do not occur, the energy resolution is lowered.

[0009] As prior art which improves on this, in the method of Tanaka etal (reference 1: Nucl. Instr. Meth. Vol. 158, pp. 459-466, 1979), thepulse time width is shortened by a delay line clipping method like thatabove, but by controlling the integration time through the occurrence ofthe succeeding pulse, so that the integration time is sufficiently longwithin the range in which the succeeding pulse does not occur, alowering in energy resolution at low count rates is avoided.

[0010] In the method of Kolodziejczyk (reference 2: U.S. Pat. No.5,430,406), by adding the pulse signal (current signal) and theintegration signal obtained by time integration of this, withappropriate weighting, an addition signal is generated which is constantin time and the amplitude of which is proportional to the energy;measurements are performed by sampling the amplitude of this additionsignal. The addition signal of the signal pulse for measurement issampled immediately before the arrival of the succeeding signal pulse;by measuring this value, the effect of pileups of succeeding signalpulses can be eliminated, but the effect of pileups of preceding signalpulses cannot be eliminated.

[0011] Still another method is that of Wong (reference 3: InternationalPatent WO98/50802). Similarly to Kolodziejczyk's method described above,this method employs a technique in which an addition signal obtainedfrom the current signal and an integration signal is measured, but isimproved so as to correct for the effect of all signal pulses arrivingbefore the signal pulse being measured.

SUMMARY OF THE INVENTION

[0012] When using a scintillation detector or other radiation detectorto measure radiation, if the count rate is high and signal pulse pileupsoccur, errors arise in measured energy values, and the energy resolutiondeclines. If signal pulse pileups occur in a gamma camera, SPECT system,PET system or other radiation image measurement system using ascintillation detector, not only the radiation energy, but the positionsign-al indicating the detected position of radiation cannot be measuredcorrectly, so that the resolution of the obtained radiation image maydecline, and distortions may appear in the image. These problems at highcount rates can be prevented to some extent using conventional pileupcorrection methods, but these methods have been inadequate.

[0013] That is, in the method described above in which pulse widths areshortened using delay line clipping, there is the drawback that energyresolution and image resolution are lowered even at low count rates atwhich pileup does not occur. In the method of Tanaka et al also, ifpulse widths are made extremely short in order to enable measurement upto high count rates, the resolution at high count rates is reduced. Inthe method of Kolodziejczyk and the method of Wong, in which the currentsignal is added to the integrated signal with appropriate weightingapplied, because the current signals of signal pulses undergo prominentstatistical fluctuations with the passage of time, there is the drawbackthat the energy resolution and image resolution are greatly reduced asthe count rate increased. Also, these methods have the further drawbackthat they can be applied only in cases in which scintillation pulsewaveforms can be approximated by a single exponential function; in othercases, for example when pulse waveforms are approximated by the sum oftwo or more exponential functions with different attenuation constants,they cannot be applied.

[0014] The present invention was devised in order to resolve the aboveproblems, and has as objects the provision of a method and apparatus formeasuring signal pulse energy which are capable of accurately andprecisely measuring the energies of individual signal pulses even athigh count rates, and improvement of the performance of radiationmeasurement and radiation image measurement.

[0015] In order to attain these objects, the energy measurement methodof this invention is an energy measurement method, in which the signalintensity of the pulse waveform of a signal pulse for measurement isintegrated and the energy of the signal pulse is measured, comprising(1) a pulse interval acquisition step, in which the pulse interval ofthe inputted signal pulse, which is the time interval from the signalpulse to the next signal pulse, is acquired; (2) an integrated intensityacquisition step, in which the signal intensity of the signal pulse isintegrated over a prescribed integration time set so as to correspond tothe pulse interval, to acquire the integrated signal intensity; and, (3)an energy calculation step, in which the energy corresponding to thetotal integrated intensity of the signal pulse is calculated from theintegrated signal intensity acquired in the integrated intensityacquisition step, and from the pulse interval acquired in the pulseinterval acquisition step; and wherein (4) in the energy calculationstep, pileup correction of the uncorrected energy calculated from theintegrated signal intensity and the pulse interval for the signal pulseto be measured is performed, using at least one of the integrated signalintensity or the energy, and the pulse interval, for the signal pulseinputted prior to the signal pulse for measurement to calculate thecorrected energy.

[0016] Also, an energy measurement apparatus of this invention is anenergy measurement apparatus which integrates the signal intensity ofthe pulse waveform of a signal pulse for measurement to measure theenergy of the signal pulse, comprising (a) trigger signal generationmeans, which accepts as input one of the branched signal pulses of theinputted signal pulse and generates a trigger signal corresponding tothe signal pulse; (b) gate signal generation means, which accepts asinput the trigger signal from the trigger signal generation means, andbased on the trigger signal, generates a gate signal to indicateintegration of the signal intensity; (c) pulse interval measurementmeans, which accepts as input the trigger signal from the trigger signalgeneration means, and measures the time interval from the trigger signaluntil the next trigger signal as the pulse interval of the signal pulse;(d) delay means, which accepts as input the other of the inputtedbranched signal pulses, and delays the signal pulse by a prescribeddelay time; (e) gate integration means, which accepts as input thesignal pulse delayed by the delay means and the gate signal from thegate signal generation means, and integrates the signal intensity of thesignal pulse for a prescribed integration time which is set based on theindication of the gate signal, to acquire the integrated signalintensity; and, (f) energy calculation means, which calculates theenergy corresponding to the total integrated intensity of the signalpulse from the integrated signal intensity acquired by the gateintegration means and from the pulse interval measured by the pulseinterval measurement means; and wherein (g) the energy calculation meansperforms pileup correction of the uncorrected energy calculated from theintegrated signal intensity and the pulse interval of the signal pulsefor measurement, using at least one of the integrated signal intensityor the energy, and the pulse interval, of the signal pulse inputtedprior to the signal pulse for measurement to calculate the correctedenergy.

[0017] In the above method and apparatus for energy measurement, theenergy is determined from the time change of the pulse waveform, thatis, of the signal intensity (current signal) of the input signal pulsefor measurement; in addition, the data previously acquired for anothersignal pulse input preceding the signal pulse to be measured is used toperform pileup correction. In this way, the effect of other signalpulses which have piled-up with the signal pulse to be measured can beeliminated, and so the energy of individual signal pulses can bemeasured correctly.

[0018] As the data used in calculation of the uncorrected energy of thesignal pulse and in pileup correction, instead of directly using thesignal pulse (current signal), which is considerably affected by noiseand other factors, the integrated signal intensity, pulse interval, andthe energy calculated from these are used. In this way, the signal pulseenergy can be measured with good precision. Thus a method and apparatusfor energy measurement is realized which makes possible the correct andprecise measurement of the energy of individual pulses, even when thepulse interval between signal pulses is short and pileup occurs amongsignal pulses.

[0019] In this specification, the “signal pulse energy” refers to thetotal integrated intensity of a signal pulse to be measured, obtained byintegrating the signal intensity over the entire pulse waveform. Thiscorresponds to the integrated signal intensity when the integration timeis made infinitely long.

BRIEF DESCRIPTION OF THE DRAWINGS

[0020]FIG. 1 is a graph which shows schematically an example of thepulse waveform of a signal pulse for energy measurement.

[0021]FIG. 2A and FIG. 2B are graphs showing the occurrence of signalpulse pileups;

[0022]FIG. 3 is a block diagram showing the configuration of a firstembodiment of an energy measurement apparatus;

[0023]FIG. 4 is a block diagram showing the configuration of a secondembodiment of an energy measurement apparatus;

[0024]FIG. 5A and FIG. 5B are graphs showing the pulse interval andeffective integration time for the pulse waveform of signal pulses;

[0025]FIG. 6 is a graph showing schematically another example of thepulse waveform of a signal pulse;

[0026]FIG. 7 is a block diagram showing the configuration of a thirdembodiment of an energy measurement apparatus;

[0027]FIG. 8 is a block diagram showing an example of the configurationof an energy calculation unit;

[0028]FIG. 9 is a block diagram showing an example of the configurationof an energy calculation unit;

[0029]FIG. 10 is a graph showing the distribution of energy valuescalculated for input signal pulses using a single exponential functioncorrection method;

[0030]FIG. 11 is a graph showing the FWHM and FWTM of energy valuescalculated for input signal pulses using a single exponential functioncorrection method;

[0031]FIG. 12 is a graph showing the FWHM and FWTM of energy valuescalculated for input signal pulses using a binomial approximationmethod, trinomial approximation method, and polynomial correctionmethod;

[0032]FIG. 13 is a graph showing the correlation between the number ofinput signal pulses and the number of outputs;

[0033]FIG. 14 is a graph showing the FWHM and FWTM of energy valuescalculated for input signal pulses using a binomial approximationmethod, trinomial approximation method, and polynomial correctionmethod;

[0034]FIG. 15A and FIG. 15B are graphs showing the distribution ofenergy values calculated for input signal pulses using (A) the trinomialapproximation method, and (B) the polynomial approximation method;

[0035]FIG. 16 is a graph showing the FWHM of energy values calculatedfor input signal pulses using the single exponential function correctionmethod and a conventional correction method;

[0036]FIG. 17A and FIG. 17B are graphs showing the distribution ofenergy values calculated for input signal pulses using (A) the singleexponential function correction method, and (B) a conventionalcorrection method;

[0037]FIG. 18 is a block diagram showing the configuration of a fourthembodiment of an energy measurement apparatus;

[0038]FIG. 19A and FIG. 19B are graphs showing the integration timesettings for performing pulse shape discrimination of signal pulses;

[0039]FIG. 20 is a graph showing a method of discrimination of pulseshapes of signal pulses;

[0040]FIG. 21A to FIG. 21C are graphs showing the distribution of energyvalues calculated for input signal pulses using pulse shapediscrimination and pileup correction;

[0041]FIG. 22 is a graph showing the FWHM and FWTM of energy valuescalculated for input signal pulses using pulse shape discrimination andpileup correction;

[0042]FIG. 23 is a graph showing the correlation between the number ofinput signal pulses and the number of outputs;

[0043]FIG. 24 is a block diagram showing the configuration of a fifthembodiment of the energy measurement apparatus; and,

[0044]FIG. 25 is a perspective view of the construction of a blockdetector for a two-dimensional position-detecting type PET system.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0045] Below, preferred embodiments of the method and apparatus forenergy measurement of this invention are explained in detail, togetherwith the drawings. In explaining the drawings, elements are assigned thesame symbols, and redundant explanations are omitted.

[0046] As examples of signal pulses for measurement by the method andapparatus for energy measurement of this invention, the graphs of timedomain waveforms of FIG. 1, FIG. 2A and FIG. 2B are used to explainsignal pulses output as detection signals from a scintillation detectorused as a radiation detector.

[0047]FIG. 1 is a graph which schematically shows one example of thetime domain waveform (current signal waveform) of the signal intensity,which is the pulse waveform, of a signal pulse output from ascintillation detector as corresponding to radiation detection. In thisgraph, the horizontal axis indicates the time t, and the vertical axisindicates the signal intensity (current value) of the signal pulse ateach time.

[0048] In the scintillation detector, an electrical signal pulse P isoutput from the photodetector connected to the scintillator according tothe light signal pulse due to the scintillation light generated withinthe scintillator. This signal pulse P generally has a pulse waveformsuch that the signal intensity, which rises at a time corresponding tothe time of scintillation light generation, is attenuated with a certainspreading in time, extending over a certain pulse time width.

[0049] Specifically, the pulse waveform of the signal pulse P exhibits apulse waveform which can, for example, be approximated as shown in FIG.1 by a signal intensity which rises at the time of the leading edge, andthen has a time domain waveform f(t) which is attenuated according to asingle exponential function with the passage of time t.

f(t)=(E/τ)exp(−t/τ).  (1)

[0050] In eq. (1), τ is the time constant for attenuation of the signalintensity in the pulse waveform of the signal pulse P, and t indicatesthe time elapsed from the leading edge of the signal pulse P. E is theenergy of the signal pulse P corresponding to the total integratedintensity of the signal intensity of the pulse waveform.

[0051] In this specification, the energy of the signal pulse refers tothe total integrated intensity of the pulse waveform of the signal pulsefor measurement, obtained by integrating the signal intensity over itsentirety. This is equivalent to the integrated signal intensity in thecase in which the integration time is made infinitely long.

[0052] When measuring the energy E of a signal pulse P, the desiredintegration time is set according to the pulse width and attenuationtime constant τ of the signal pulse P, and the signal intensity of thepulse waveform f(t) is integrated over the integration time thus set. Ifthe integration time for integrating the signal intensity starting fromthe leading edge of the signal pulse P is T. then the integrated signalintensity Q(T), which is the integrated charge amount thus obtained, isexpressed by $\begin{matrix}{{Q(T)} = {{\int_{0}^{T}{{f(t)}{t}}} = {E{\left\{ {1 - {\exp \left( {{- T}/\tau} \right)}} \right\}.}}}} & (2)\end{matrix}$

[0053] This integrated signal intensity Q(T) is equivalent to theintegrated value of the signal intensity over the range indicated by theshading in FIG. 1; as the integration time T is lengthened, theintegrated signal intensity approaches the energy E of the signal pulseP, which is the total integrated intensity. If, for convenience inexpression, the integration response G(T) is defined as

G(T)=1−exp(−T/τ)  (3)

[0054] then the integrated signal intensity of eq. (2) becomesQ(T)=EG(T).

[0055]FIG. 2A and FIG. 2B are graphs showing the occurrence of signalpulse pileups. Such signal pulse pileups occur when, for example, thenumber of detections (count rate) per unit time of radiation in thescintillation detector is high, and the pulse time interval betweensignal pulses is short. In other words, when the pulse interval betweensignal pulses becomes substantially the same as or shorter than thepulse widths of individual signal pulses, pileups occur, in which thepulse waveforms of two or more signal pulses P overlap, as shown in thegraph of time domain waveforms of FIG. 2A.

[0056] In the graph of FIG. 2A, the two signal pulses P₁, P₂continuously preceding the signal pulse P₀, shown as the signal pulsethe energy of which is to be measured, are shown with pulse waveformssimilar to the pulse waveform of the signal pulse P₀. These signalpulses P₁ and P₂ are both piled-up with the signal pulse P₀ which is tobe measured.

[0057] Here, if the time at the leading edge of the signal pulse P₀ is0, then the times at the leading edge of the signal pulse P₁ is taken tobe −t₁, and the time at the leading edge of the signal pulse P₂ is takento be −t₂ (−t₂<−t₁<0), as shown in FIG. 2A. Also, the pulse intervalfrom the signal pulse for measurement to the next signal pulse isassumed to be T₂ at the signal pulse P₂, T₁ at the signal pulse P₁, andT₀ at the signal pulse P₀.

[0058] Suppose that, for the pulse waveforms of each of these signalpulses P_(i) (i=2,1,0), integration of the signal intensity isperformed, taking as the integration time the pulse interval T_(i) untilthe next signal pulse. Then the integrated signal intensity Q₀(T₀)resulting from integration over the integration time T₀ is obtained asthe integrated signal intensity for the signal pulse P₀ (the integrationvalue over the range indicated by shading in FIG. 2A). Similarly,integrated signal intensities Q₁(T₁), Q₂(T₂) resulting from integratingover the integration times T₁, T₂ are obtained as the integrated signalintensities of the signal pulses P₁, P₂.

[0059] The energy E₀ of the signal pulse P₀ to be measured is equivalentto the integrated signal intensity, resulting from integration of theentirety of the signal intensity contained in the pulse waveform of thesignal pulse P₀, as shown by the shading in FIG. 2B. If the frequency ofsignal pulses is low and pileup does not occur, then if the pulsewaveform f(t) of the signal pulse to be measured is known, the above eq.(2) can be used to calculate the energy E₀=Q₀/G(T₀) of the signal pulseP₀ from the integrated signal intensity Q₀ and the pulse interval T₀which is the integration time.

[0060] On the other hand, when signal pulse pileups occur, theintegrated signal intensity Q₀ actually obtained for a signal pulse P₀includes, in addition to the integration value of the signal intensityfor the signal pulse P₀ itself, the integration values of the signalintensity for the other signal pulses P₁, P₂ which precede the signalpulse P₀ and are piled-up with the signal pulse P₀, as shown in FIG. 2A.Here the integrated signal intensity Q₀ does not correspond directly tothe signal intensity of the signal pulse P₀ or to the energy E₀ which isthe total integrated intensity. Hence if this integrated signalintensity Q₀ is used without modification, the energy E₀ of the signalpulse P₀ cannot be measured correctly.

[0061] Thus when signal pulse pileup occurs, in order to correctlymeasure the energy E of a signal pulse P, when calculating the energy Epileup correction must be performed, in which the effect of other signalpulses which are piled-up with the signal pulse P being measured iseliminated.

[0062] The method and apparatus for energy measurement of this inventionenable the correct and precise measurement of the energy of individualsignal pulses even when pileup of signal pulses occurs; by using aprescribed method and configuration to perform such pileup correction.

[0063]FIG. 3 is a block diagram showing the configuration of a firstembodiment of an energy measurement apparatus of this invention. Theenergy measurement apparatus 1 is an energy measurement circuit (signalprocessing circuit) which measures the energy E of a signal pulse P byintegrating the signal intensity of the pulse waveform of a signal pulseP input for measurement, and comprises an energy calculation unit 10which performs operations and similar to calculate the energy E of thesignal pulse P.

[0064] The signal pulse P for energy measurement, which is for examplethe electrical signal pulse which is a detection signal from ascintillation detector as shown in FIG. 1, FIG. 2A, and FIG. 2B, isinput to the energy measurement apparatus 1, and is branched into twosignal pulses.

[0065] One of the branched signal pulses is input to the trigger signalgenerator 21. The trigger signal generator 21 generates a trigger signalcorresponding to the signal pulse P. Specifically, for example, athreshold is set in advance as the lower limit of the signal intensityfor the pulse waveform of the input signal pulse P, and when the signalintensity of the signal pulse P exceeds the threshold, a trigger signalcorresponding to the signal pulse P is generated and output.

[0066] The trigger signal output from the trigger signal generator 21 isinput to the gate signal generator 22 and pulse interval measurementunit 23. The gate signal generator 22 generates a gate signal toinstruct integration (for example, to instruct that integration bestarted or stopped) of the signal intensity of the signal pulse P, basedon the trigger signal. The pulse interval measurement unit 23 measuresthe time interval from the trigger signal until the next trigger signal,taking T as the pulse interval from the signal pulse P to be measureduntil the next signal pulse.

[0067] On the other hand, the other branched signal pulse is input tothe delay circuit 31. The delay circuit 31 delays the input signal pulseP by a prescribed delay time before output, in order to performintegration of the signal intensity based on instruction by the gatesignal.

[0068] The signal pulse P thus delayed by the delay circuit 31 is inputto the gate integrator 32. A gate signal from the gate signal generator22 is also input to the gate integrator 32. The gate integrator 32performs integration of the signal intensity of the signal pulse P inputfrom the delay circuit 31, for a prescribed integration time set basedon the instruction of this gate signal, and outputs the integratedsignal intensity Q thus obtained.

[0069] The integrated signal intensity Q obtained by the above gateintegrator 32, and the pulse interval T measured by the pulse intervalmeasurement unit 23, are input to the energy calculation unit 10 whichcalculates the energy E of the signal pulse P. The energy calculationunit 10 calculates the energy E corresponding to the total integratedintensity of the signal pulse P from the integrated signal intensity Qand pulse interval T, while performing pileup correction so as toeliminate the influence of other signal pulses which have piled-up withthe signal pulse P.

[0070] The method of measuring the energy of the signal pulse P executedby the energy measurement apparatus 1 of this embodiment may besummarized as follows (cf. FIG. 2A).

[0071] First, the pulse interval T₀ from a signal pulse P₀, input to theenergy measurement apparatus 1 for measurement, to the next signalpulse, is acquired in the pulse interval measurement unit 23 (pulseinterval acquisition step). Also, the integrated signal intensity Q₀ isacquired by the gate integrator 32 by integrating the signal intensityof the signal pulse P₀ over a prescribed integration time, set so as tocorrespond to the pulse interval T₀ based on the instruction of a gatesignal (integrated intensity acquisition step).

[0072] The energy E₀ of the signal pulse P₀ is then calculated in theenergy calculation unit 10 from this integrated signal intensity Q₀ andpulse interval T₀ (energy calculation step).

[0073] At this time, pileup correction is performed on the uncorrectedenergy calculated from the integrated signal intensity Q₀ and pulseinterval T₀ for the signal pulse P₀ to be measured, using a pulseinterval (for example, the pulse interval T₁), and either an integratedsignal intensity (for example, the integrated signal intensity Q₁) or anenergy (for example, the energy E₁), or both, previously acquired, for asignal pulse input before the signal pulse P₀ (for example, the signalpulse P₁). By this means, a corrected energy E₀ is calculated in whichthe effect of other signal pulses piled-up on the signal pulse P₀ isgreatly eliminated, and is output from the energy measurement apparatus1.

[0074] Below the advantageous results of the above-described method andapparatus for energy measurement are explained.

[0075] In the method and the apparatus 1 for energy measurement of thisembodiment, the energy E of the input signal pulse P for measurement isdetermined from the pulse waveform, that is, from the time change in thesignal intensity, and in addition data acquired previously for othersignal pulses input before the signal pulse P is used to perform pileupcorrection. By this means, the effect of other signal pulses which havepiled-up on the signal pulse P is eliminated, and the energy E ofindividual signal pulses P can be correctly measured.

[0076] As data used in calculation of the energy of the signal pulse Pprior to correction and in pileup correction, instead of directly usingthe signal intensity of the signal pulse P, which is greatly influencedby the noise signal arising in the signal pulse P and other factors, theintegrated signal intensity Q obtained by integration of the signalintensity by the gate integrator 32, the pulse interval T measured bythe pulse interval measurement unit 23, and the energy E calculated fromthese, are used in energy calculations. By this means, the energy E ofthe signal pulse P can be measured with good precision.

[0077] Thus a method and apparatus for energy measurement is realizedwhich are capable of the correct and precise measurement of the energiesof individual signal pulses, even when the pulse interval between signalpulses is short, and pileups occur between signal pulses. Such a methodis not limited to cases in which the pulse waveforms of signal pulsesare expressed by a single exponential function, but can be applied to awide range of more general time domain waveforms.

[0078] Various devices may be used as necessary as the respectivecircuit elements comprised by the energy measurement apparatus 1. Forintegration of the signal intensity by the gate integrator 32, analogoperation may be used to integrate the current signal; or, aftercontinuous sampling to digitize the signal waveform, digital operationmay be employed for integration. In measurement of pulse intervals bythe pulse interval measurement unit 23, a method can be used in which aclock pulse is for example be input to the pulse interval measurementunit 23, so that by counting the number of clock pulses, the timeinterval is measured.

[0079] Below a more specific explanation of the configuration of theenergy measurement apparatus, and of the energy measurement methodincluding the method of energy calculation executed by the measurementapparatus, is given.

[0080]FIG. 4 is a block diagram showing the configuration of a secondembodiment of the energy measurement apparatus. This energy measurementapparatus 1 is configured to enable application to measurement of theenergy of a signal pulse when the pulse waveform of the signal pulse Pfor measurement can be represented, for example, by a single exponentialfunction, as shown for example in FIG. 1, FIG. 2A and FIG. 2B.

[0081] The energy measurement apparatus 1 of this embodiment is similarto the embodiment shown in FIG. 3 with respect to the trigger signalgenerator 21, gate signal generator 22, pulse interval measurement unit23, delay circuit 31, and gate integrator 32.

[0082] The energy calculation unit 10 in this embodiment has an energycomputing unit 11, lookup table 12, and two buffer memories 40, 41. Theenergy computing unit 11 performs computations necessary to calculatethe energy E₀ corresponding to the input signal pulse P₀ to be measured.As explained below, the lookup table 12 stores coefficient data used incomputations executed by the energy computing unit 11.

[0083] The buffer memory 40 stores an integrated signal intensity Q₀input from the gate integrator 32 and a pulse interval T₀ input from thepulse interval measurement unit 23, in association with the signal pulseP₀ which is to be measured at each moment. The buffer memory 41 storesthe integrated signal intensity Q₁ and pulse interval T₁ of the signalpulse P₁ preceding the signal pulse P₀. Each of these data sets is datainput for computations by the energy computing unit 11 to calculate theenergy.

[0084] By thus configuring an energy calculation unit 10 having anenergy computing unit 11 which performs computations in order tocalculate the energy E₀, a buffer memory 40 (first buffer memory) whichstores the integrated signal intensity Q₀ and pulse interval T₀ of thesignal pulse P₀ to be measured, and a buffer memory 41 (second buffermemory) which stores the integrated signal intensity Q₁ and pulseinterval T₁ of the signal pulse P₁ preceding the signal pulse P₀,computations to calculate the energy E can be reliably performed, whilereferring to the data stored in the buffer memories.

[0085] Below is explained the single exponential function correctionmethod, which is a method for calculation of the energy E which can beapplied to cases in which the pulse waveform of the signal pulse P isexpressed by a single exponential function such as the time domainwaveform f(t) in eq. (1), referring to the energy measurement apparatusshown in FIG. 4 and in particular to the configuration of the energycalculation unit 10.

[0086] When the pulse waveform of the signal pulse P₀ is expressed bythe time domain waveform f(t) of eq. (1), if it is supposed that pileupof signal pulses does not occur, then the integrated signal intensityQ₀, obtained by integrating the signal intensity with the pulse intervalT₀ as the integration time, is

Q ₀ =E ₀{1−exp(−T ₀/τ)}=E ₀ G(T ₀).  (4)

[0087] Here the energy E₀ of the signal pulse P₀ is calculated from theintegrated signal intensity Q₀ and pulse interval T₀ stored in thebuffer memory 40 using $\begin{matrix}{E_{0} = {\frac{Q_{0}}{G\left( T_{0} \right)}.}} & (5)\end{matrix}$

[0088] On the other hand, when pileup of signal pulses occurs, theintegrated signal intensity Q₀ includes the integrated signalintensities of signal pulses P₁, P₂, and similar preceding the signalpulse P₀. Hence in order to correctly determine the energy E₀, pileupcorrection, in which the integrated signal intensities of the signalpulses P₁, P₂ and similar are eliminated from the right-hand sideQ₀/G(T₀) in eq. (5), must be performed. When pulse waveforms are asingle exponential function, the integrated signal intensities to beremoved can be determined from the integrated signal intensity Q₁ andpulse interval T₁ stored in the buffer memory 41 as data previouslyacquired for the signal pulse P₁ immediately preceding the signal pulseP₀ being measured.

[0089] From the above, in a single exponential function correctionmethod, the pileup-corrected energy E₀ of a signal pulse P₀ can becalculated using the following eq. (6) from the integrated signalintensity Q₀ and pulse interval T₀ stored in the buffer memory 40, andthe integrated signal intensity Q₁ and pulse interval T₁ stored in thebuffer memory 41. $\begin{matrix}{E_{0} = {\frac{Q_{0}}{G\left( T_{0} \right)} - {Q_{1}{\frac{\exp \left( {{- T_{1}}/\tau} \right)}{G\left( T_{1} \right)}.}}}} & (6)\end{matrix}$

[0090] In the above eq. (6), the pulse interval T_(i) until the nextsignal pulse is used without modification as the integration time forintegrating the signal intensity of each signal pulse P_(i). Inactuality, however, the integration time must be set taking into accountthe fact that some time is required to read and reset integration valuesin the gate integrator 32. Also, it is preferable that a maximumintegration time be set as an upper limit on the integration time, inorder that integration of signal intensity is not performed over a longperiod of time when the pulse interval T_(i) is long.

[0091] If the reset time required for reading and reset of anintegration value in the gate integrator 32 is T_(r), and the maximumintegration time set is T_(max), then the effective integration time T′for actual integration of the signal intensity as a function of thepulse interval T of the signal pulse P is:

T′=min(T _(max) , T−Tr).  (7)

[0092]FIG. 5A and FIG. 5B are graphs showing the pulse interval T andeffective integration time T′ for the pulse waveform of the signal pulseP. Similarly to FIG. 2A, the graph of FIG. 5A shows the signal waveform,which is the change with time in the signal intensity. The graph of FIG.5B shows the integrated waveform, which is the change in time of theintegrated signal waveform, obtained by integrating the signal waveformshown in FIG. 5A.

[0093] In FIG. 5A and FIG. 5B, as an example, a case is shown in whichthe pulse interval T₀ for the signal pulse P₀ satisfies the relationwith the maximum integration time T_(max) of T₀−T_(r)<T_(max). Here theeffective integration time T₀′ for the pulse interval T₀ of the signalpulse P₀ is T₀′=T₀−T_(r). The integrated signal intensity output fromthe gate integrator 32 has an integration waveform which increases withintegration of the signal waveform of the signal pulse P₀ over theeffective integration time T₀′ from the start of integration, as shownin FIG. 5B. This is then reset for the reset time T_(r) until the startof integration of the next signal pulse, and acquisition of theintegrated value in the gate integrator 32 is executed.

[0094] In this way, by using as the integration time for the signalintensity the effective integration time T′, the integration time can beprevented from becoming very long, and in addition, integration timesappropriate to the pulse intervals T can be set for respective signalpulses P, so as to greatly increase the precision of the calculatedenergy E. The maximum integration time T_(max) is set to, for example,approximately 3τ, where τ is the attenuation time constant of the pulsewaveform f(t).

[0095] This effective integration time T′ is set to the maximumintegration time T_(max) in cases where the pulse interval T is long;when the pulse interval T is short, however, it may be set to theminimum pulse interval to execute calculation of the energy E. Here, theminimum pulse interval should preferably be set with respect to thepulse interval T₁ preceding the signal pulse P₀ for measurement, and thesucceeding pulse interval T₀.

[0096] By providing a minimum pulse interval for the previous pulseinterval T₁, cases in which the pile-up of the preceding signal pulse P₁with the signal pulse P₀ is too large can be eliminated. Also, byproviding a minimum pulse interval for the succeeding pulse interval T₀,cases in which a sufficient integration time for the signal pulse P₀cannot be secured can be eliminated.

[0097] In applying the above effective integration time T′, in place ofthe integration response G(T) for the pulse interval T, if an effectiveintegration response H(T) is defined for the effective integration timeT′, then this H(T) is expressed as:

H(T)=G(T′)=1−exp(−T′/τ).  (8)

[0098] The pileup-corrected energy E₀ for the signal pulse P₀ can becalculated using the following eq. (9), obtained by modifying the aboveeq. (6) using this effective integration response H(T). $\begin{matrix}{\begin{matrix}{E_{0} = {\frac{Q_{0}}{H\left( T_{0} \right)} - {Q_{1}\frac{\exp \left( {{- T_{1}}/\tau} \right)}{H\left( T_{1} \right)}}}} \\{= {{Q_{0} \cdot {A\left( T_{0} \right)}} - {Q_{1} \cdot {{B\left( T_{1} \right)}.}}}}\end{matrix}\quad} & (9)\end{matrix}$

[0099] In this eq. (9), A(T) is a coefficient used to calculate theenergy E₀ corresponding to the total integrated intensity from theintegrated signal intensity Q₀ obtained from the gate integrator 32; itsvalue is determined based on the pulse interval T₀ of the signal pulseP₀. Also, B(T) is a coefficient used in pileup correction using theintegrated signal intensity Q₁ for the signal pulse P₁ immediatelypreceding; its value is determined based on the pulse interval T₁ of thesignal pulse P₁.

[0100] From the above, by determining the coefficients A(T₀) and B(T₁)referring to the pulse intervals T₀ and T₁, the correct energy E₀ of thesignal pulse P₀ can be easily calculated in the energy computing unit 11from the integrated signal intensity Q₀ stored in the buffer memory 40and the integrated signal intensity Q₁ stored in the buffer memory 41.

[0101] Here it is preferable that the values of each of the coefficientsA(T) and B(T) used in calculating the energy E₀ be determined in advancefrom the values of a plurality of pulse intervals T, and that a lookuptable 12 (cf. FIG. 4) be created from the values of the coefficients. Bythis means, the values of the coefficients A(To) and B(T₁) can be readfrom two lookup tables contained in the lookup table 12, a lookup tablefor the coefficient A(T) and a lookup table for the coefficient B(T),for the acquired pulse intervals T₀ and T₁, and the pileup-correctedenergy E₀ can be quickly and efficiently calculated.

[0102] Next, the case in which the pulse waveform of the signal pulse Pis a general time domain waveform (general waveform) which cannot beexpressed as a single exponential function is explained.

[0103] A general waveform of a signal pulse output from a scintillationdetector to correspond to radiation detection may, for example, beexpressed as the sum of a plurality of exponential functions withdifferent attenuation time constants. As an example of the pulsewaveform of a signal pulse having a general waveform, FIG. 6 is a graphshowing schematically a pulse waveform f(t)=Eg(t), including a componentwith a small attenuation time constant and which attenuates rapidly, anda component with a large attenuation time constant and which attenuatesslowly.

[0104] In pileup correction of a signal pulse having such a generalwaveform, due to differences in the time domain waveforms, the above eq.(6) or eq. (9) cannot be applied; however, the signal intensity (chargeamount) due to the preceding signal pulse piled-up with the signal pulseto be measured can be inferred from the signal pulse energy, previouslymeasured, of another signal pulse, and pileup correction can besimilarly performed.

[0105]FIG. 7 is a block diagram showing the configuration of a thirdembodiment of an energy measurement apparatus. This energy measurementapparatus 1 has a configuration which can be applied to measurement ofthe energy of a signal pulse having a general waveform which cannot berepresented as a single exponential function, as for example in theexample of the pulse waveform of a signal pulse P for measurement likethat shown in FIG. 6.

[0106] In the energy measurement apparatus 1 of this embodiment, thetrigger signal generator 21, gate signal generator 22, pulse intervalmeasurement unit 23, delay circuit 31, and gate integrator 32 aresimilar to those of the embodiment shown in FIG. 3.

[0107] The energy calculation unit 10 in this embodiment has an energycomputing unit 11, lookup table 12, data input-side buffer memory 45,and energy output-side buffer memory 50. The energy computing unit 11performs computations necessary to calculate the energy E₀ correspondingto the input signal pulse P₀ for measurement. The lookup table 12 storescoefficient data to be used in computations executed by the energycomputing unit 11.

[0108] The data input-side buffer memory 45 stores the integrated signalintensity Q₀ input from the gate integrator 32 and the pulse interval T₀input from the pulse interval measurement unit 23, corresponding to thesignal pulse P₀ for measurement at each moment. Also, the pulseintervals T₁, T₂, . . . , T_(J) for J signal pulses P₁, P₂, . . . ,P_(J) (where J is an integer equal to or greater than 1) continuouslypreceding the signal pulse P₀ are stored. The energy output-side buffermemory 50 stores the energy E₀ calculated for the signal pulse P₀; alsostored are the energies E₁, E₂, . . . , E_(J) for J signal pulses P₁,P₂, . . . , P_(J) preceding the signal pulse P₀. These data values areinput data for computations to calculate the energy by the energycomputing unit 11.

[0109] A polynomial correction method, which is a method for computingthe energy E that can be applied to cases in which the pulse waveform ofthe signal pulse P is a general waveform, is explained below, referringto the configuration of the energy measurement apparatus 1 shown in FIG.7, and in particular to the configuration of the energy calculation unit10.

[0110] As shown in the example of FIG. 6, if it is assumed that thepulse waveform of the signal pulse P is a general time domain waveformexpressed by f(t)=Eg(t), then the integration response G(T)corresponding to the integration response appearing in eq. (3) for thecase of a single exponential function becomes $\begin{matrix}{{G(T)} = {\int_{0}^{T}{{g(t)}{{t}.}}}} & (10)\end{matrix}$

[0111] Applying the effective integration time T′ of eq. (7), takinginto account the reset time T_(r) in the gate integrator 32 and maximumintegration time T_(max), the effective integration response H(T)corresponding to the effective integration response in eq. (8) isexpressed by: $\begin{matrix}{{H(T)} = {{G\left( T^{\prime} \right)} = {\int_{0}^{T^{\prime}}{{g(t)}{{t}.}}}}} & (11)\end{matrix}$

[0112] The pileup-corrected energy E₀ of the signal pulse P₀ can becalculated as in the following eq. (12), using this effectiveintegration response H(T): $\begin{matrix}{\begin{matrix}{E_{0} = {\frac{Q_{0}}{H\left( T_{0} \right)} - {\sum\limits_{j = 1}^{J}{E_{j}{H\left( {t_{j} + T_{0}} \right)}}} - \frac{H\left( t_{j} \right)}{H\left( T_{0} \right)}}} \\{= {{Q_{0} \cdot {C_{0}\left( T_{0} \right)}} - {\sum\limits_{j = 1}^{J}{E_{j} \cdot {{C_{j}\left( T_{j} \right)}.}}}}}\end{matrix}\quad} & (12)\end{matrix}$

[0113] Here J is the number of signal pulses P₁, . . . , P_(J), inputprevious to the signal pulse P₀ for measurement, that are used in pileupcorrection. This number J also corresponds to the number of values ofthe previous pulse intervals T₁, . . . , T_(J) stored in the abovebuffer memory 45, and the number of values of the previous energies E₁,. . . , E_(J) stored in the buffer memory 50.

[0114] In eq. (12), C₀(T) is a coefficient used to calculate the energyE₀ corresponding to the total integrated intensity from the integratedsignal intensity Q₀ obtained from the gate integrator 32; its value isdetermined based on the pulse interval T₀ of the signal pulse P₀. Also,C_(j)(T_(j))=C_(j)(t_(j), T₀) (j=1, . . . , J) are coefficients used toperform pileup correction, using the energies E_(j) of the J signalpulses P_(j) preceding the signal pulse P₀, and are determined based onthe pulse intervals T_(j) of the signal pulses P_(j). Also, t_(j)corresponds to the time of the leading edge of the signal pulse P_(j) ifthe time of the leading edge of the signal pulse P₀ is 0 (cf. FIG. 2A);expressed in terms of the pulse intervals T_(j), it can be written:

t _(J) =T ₁ +T ₂ + . . . +T _(J).  (13)

[0115] Thus by determining the coefficients C₀(T₀) and C_(j)(T_(j)) inthe energy computing unit 11, referring to the pulse intervals T₀, T₁, .. . , T_(J), the energy E₀ of the signal pulse P₀ can easily bedetermined accurately from the integrated signal intensity Q₀ stored inthe buffer memory 45 and from the energies E₁, . . . , E_(J) stored inthe buffer memory 50, even in cases where the pulse waveform of thesignal pulse P₀ is a general waveform.

[0116] Here it is preferable that the values of each of the coefficientsC₀(T) and C_(j)(T) (j=1, . . . , J) used in calculating the energy E₀ bedetermined in advance for a plurality of values of the pulse interval T,and that a lookup table 12 (cf. FIG. 7) be created from thesecoefficient values. By this means, the pileup-corrected energy E₀ can becalculated quickly and efficiently.

[0117] The larger the number J of signal pulses used in pileupcorrection, the more the precision of pileup correction, and thereforethe precision of the calculated energy E₀ is improved. In actualpractice, it is preferable that an appropriate number J be set inconsideration of the pulse waveform of the signal pulses formeasurement, the frequency of input of signal pulses, the time requiredfor computations to calculate the energy E₀, the amount of data in thelookup table prepared, and other factors.

[0118] As explained above, the method for calculating the energy usingthe eq. (12) for a general waveform is a polynomial correction methodwhich performs pileup correction using J signal pulses preceding thesignal pulse P₀. Except for the fact that the effect of the J+1th andsubsequent signal pulses is ignored, this eq. (12) is an accurateexpansion of the energy E₀. On the other hand, in order to simplify theenergy computations and reduce the number of data values used incomputations, it is also possible to use a binomial approximationmethod, a trinomial approximation method or similar to perform pileupcorrection for a general waveform.

[0119] In a binomial approximation method, the electric charge of signalpulses prior to the signal pulse P₂ is ignored (cf. FIG. 2A) incalculating the energy E₀ of the signal pulse P₀, and it is assumed thatthe amount of electric charge from the time −t₁ of the leading edge ofthe preceding signal pulse P₁ to the time 0 of the leading edge of thesignal pulse P₀ is entirely due to the signal pulse P₁. At this time,the energy E₀ of the signal pulse P₀ after pileup correction can bedetermined approximately using the following eq. (14): $\begin{matrix}{\begin{matrix}{E_{0} = {\frac{1}{H\left( T_{0} \right)}\left\lbrack {Q_{0} - {Q_{1}{H\left( {t_{1} + T_{0}} \right)}} - {\frac{H\left( t_{1} \right)}{H\left( T_{1} \right)} \cdot x}} \right\rbrack}} \\{= {{Q_{0} \cdot {D_{0}\left( T_{0} \right)}} - {Q_{1} \cdot {{D_{1}\left( T_{1} \right)}.}}}}\end{matrix}\quad} & (14)\end{matrix}$

[0120] Here x is a correction coefficient determined empiricallyaccording to the pulse waveform.

[0121]FIG. 8 is a block diagram showing an example of the configurationof an energy calculation unit, corresponding to an energy calculationmethod using the binomial approximation method of eq. (14). This energycalculation unit 10 has an energy computing unit 11; lookup table 12;and two data input-side buffer memories 40, 41. Except for the detailsof computations executed by the energy computing unit 11, thisconfiguration is equivalent to that shown in FIG. 4.

[0122] The buffer memory 40 stores the integrated signal intensity Q₀and pulse interval T₀ corresponding to the signal pulse P₀ to bemeasured at each moment. The buffer memory 41 stores the integratedsignal intensity Q₁ and pulse interval T₁ for the signal pulse P₁.

[0123] The energy computing unit 11 determines the coefficients D₀(T₀)and D₁(T₁), referring to the pulse intervals T₀ and T₁, or reads thevalues of the coefficients D₀(T₀) and D₁(T₁) from the lookup table 12.By this means, the pileup-corrected energy E₀ can be calculated from eq.(14) using the integrated signal intensity Q₀ stored in the buffermemory 40 and the integrated signal intensity Q₁ stored in the buffermemory 41.

[0124] In a trinomial approximation method, the electric charge ofsignal pulses preceding the signal pulse P₃ is ignored when calculatingthe energy E₀ of the signal pulse P₀; the effect of the energy E₁ of thesignal pulse P₁ is corrected properly, and in addition it is assumedthat the electric charge from the time −t₂ of the leading edge of thesignal pulse P₂ until the time −t₁ of the leading edge of the signalpulse P₁ is assumed to be entirely due to the signal pulse P₂. At thistime, the energy E₀ of the signal pulse P₀ after pileup correction canbe calculated approximately using the following eq. (15);$\begin{matrix}{\begin{matrix}{E_{0} = {\frac{1}{H\left( T_{0} \right)}\left\lbrack {Q_{0} - {E_{1}\left\{ {{H\left( {t_{1} + T_{0}} \right)} - {H\left( t_{1} \right)}} \right\}} - {Q_{2}{H\left( {t_{2} + T_{0}} \right)}} - {\frac{H\left( t_{2} \right)}{H\left( T_{2} \right)} \cdot x}} \right\rfloor}} \\{= {{Q_{0} \cdot {D_{0}\left( T_{0} \right)}} - {E_{1} \cdot {D_{1}\left( T_{1} \right)}} - {Q_{2} \cdot {{D_{2}\left( T_{2} \right)}.}}}}\end{matrix}\quad} & (15)\end{matrix}$

[0125] Here x is a correction coefficient determined empiricallyaccording to the pulse waveform.

[0126]FIG. 9 is a block diagram showing an example of the configurationof an energy calculation unit, corresponding to an energy calculationmethod using the trinomial approximation method of eq. (15). This energycalculation unit 10 has an energy computing unit 11; a lookup table 12;three data input-side buffer memories 40, 41, 42; and an energyoutput-side buffer memory 50.

[0127] The data input-side buffer memory 40 stores the integrated signalintensity Q₀ and pulse interval T₀ corresponding to the signal pulse P₀for measurement at each moment. The buffer memory 41 stores theintegrated signal intensity Q₁ and pulse interval T₁ of the signal pulseP₁. And the buffer memory 42 stores the integrated signal intensity Q₂and pulse interval T₂ of the signal pulse P₂. The energy output-sidebuffer memory 50 stores the energy E₀ of the signal pulse P₀ and theenergy E₁ of the signal pulse P₁.

[0128] The energy computing unit 11 determines the coefficients D₀(T₀),D₁(T₁) and D₂(T₂), referring to the pulse intervals T₀, T₁, and T₂, orreads the values of the coefficients D₀(T₀), D₁(T₁) and D₂(T₂) from thelookup table 12. By this means, the pileup-corrected energy E₀ can bedetermined using eq. (15) from the integrated signal intensity Q₀ storedin the buffer memory 40, the energy E₁ stored in the buffer memory 50,and the integrated signal intensity Q₂ stored in the buffer memory 42.

[0129] Simulations were performed of energy measurements using, asmethods of energy calculation, the above-described single exponentialfunction correction method, polynomial correction method, binomialapproximation method, and trinomial approximation method, and theresults of each were confirmed. In these simulations, numerous signalpulses having a prescribed pulse waveform and energy were generated in atimewise-random manner with a prescribed average count rate, calculatedvalues for energies were simulated based on the prescribed energycalculation methods and pileup correction methods, and the average pulseheight distribution and energy resolution were estimated. The energy forindividual pulse signals was expressed as the total number ofphotoelectrons collected by the first dynode of the photomultipliertube, and the energy of measured pulse signals was assumed to undergostatistical fluctuations according to a Poisson distribution of thenumber of photoelectrons collected within the prescribed integrationtime. It was assumed that pulse intervals were accurately measured, andthe error in measuring pulse intervals and errors due to digitizationwere ignored.

[0130] Simulation results for energy calculations and pileup correctionusing the single exponential function correction method are firstexplained, referring to FIGS. 10 and 11. Here, it was assumed that thepulse waveform of the signal pulse P was a time domain waveformcomprising a single exponential function component with an attenuationtime constant τ=240 ns, and the energy, expressed as a number ofphotoelectrons, was taken to be 1000. As other conditions, the resettime was set at T_(r)=50 ns, and the maximum integration time atT_(max)=1000 ns.

[0131]FIG. 10 is a graph showing the distribution of energy valuescalculated for input signal pulses using the single exponential functioncorrection method. In this graph, the horizontal axis indicates thecalculated value (channel) for the energy E of the signal pulse P, andthe vertical axis indicates the number of counts per channel.

[0132] In FIG. 10, the energy distribution shown was obtained byconducting simulations under four conditions, with input count rates at(1) 0.01 Mcps, (2) 1 Mcps, (3) 2.5 Mcps, and (4) 5 Mcps. As the inputcount rate increases, the energy resolution declines somewhat, but as aresult of pileup correction, energy shifts and declines in energyresolution due to integration of the signal intensity of other signalpulses are suppressed.

[0133]FIG. 11 is a graph showing the full width at half-maximum (FWHM)and the full width at 10% of maximum (FWTM) of energy values calculatedfor input signal pulses using the single exponential function correctionmethod. From these graphs also, it is seen that by performing pileupcorrection using a single exponential function correction method forsignal pulses having a pulse waveform that is a single exponentialfunction, the decline in energy resolution accompanying increases in thenumber of input signal pulses can be greatly suppressed.

[0134] Next, results of the first simulation of energy calculations andpileup correction using the binomial approximation method, trinomialapproximation method, and polynomial correction method are explained,referring to FIGS. 12 and 13. As the pulse waveform of the signal pulsesP, a general time domain waveform was assumed having a first exponentialfunction component with an attenuation time constant τ₁=240 ns, and asecond exponential function component with τ₂=50 ns, with the ratio ofintensities 70%:30%. As other conditions, the reset time was set toT_(r)=50 ns and the maximum integration time T_(max) to 1000 ns, and theenergy, expressed as the number of photoelectrons, was assumed to be2000.

[0135]FIG. 12 is a graph showing the FWHM and FWTM of energy valuescalculated for input signal pulses using the binomial approximationmethod, trinomial approximation method, and polynomial correctionmethod. In the binomial approximation method, the correction coefficientwas taken to be x=1.1. In the trinomial approximation method, thecorrection coefficient was set to x=1.2. In the polynomial correctionmethod, the number of signal pulses used in pileup correction was set toJ=5.

[0136] From these graphs, it is seen that by using the binomialapproximation method, trinomial approximation method, and polynomialcorrection method to perform pileup correction for signal pulses havinga general pulse waveform, a decline in energy resolution accompanyingincreases in the number of input signal pulses can be greatlysuppressed.

[0137] On comparing the binomial approximation method, trinomialapproximation method, and polynomial correction method, by increasingthe number of terms in pileup correction from two to three, and then tomany (J=5), the precision of the calculated energy value is improved.

[0138]FIG. 13 is a graph showing the correlation between the input countrate and the output count rate in the above simulation results, that is,the count rate characteristic. As a result of setting the minimumintegration time to 100 ns, only those signal pulses for which the pulseinterval, both preceding and following, is 100 ns (total 200 ns) or moreare detected; hence a state of saturation is seen at an output countrate of 5 Mcps.

[0139] Next, results of the second simulation of energy calculations andpileup correction using the binomial approximation method, trinomialapproximation method, and polynomial correction method are explained,referring to FIGS. 14, 15A, and 15B. Here, as the pulse waveform of thesignal pulses P, a general time domain waveform was assumed having afirst exponential function component with an attenuation time constantτ₁=1000 ns, a second exponential function component with τ₂=210 ns, anda third exponential function component with τ₃=26 ns, and with the ratioof intensities 30%:30%:40%. Other conditions are similar to those ofFIGS. 12 and 13.

[0140]FIG. 14 is a graph showing the FWHM and FWTM of energy valuescalculated for input signal pulses using a binomial approximationmethod, trinomial approximation method, and polynomial correctionmethod. In the binomial approximation method, the correction coefficientwas set to x=1.7; in the trinomial approximation method, the correctioncoefficient was set to x=2.0. And in the polynomial correction method,the number of signal pulses used in pileup correction was set to J=5(polynomial 1) and J=10 (polynomial 2).

[0141] From this graph, similarly to the graph of FIG. 12, it is seenthat by performing pileup correction of signal pulses having a generalpulse waveform, using the binomial approximation method, trinomialapproximation method, or the polynomial correction method, reductions inenergy resolution accompanying an increase in the number of input signalpulses can be greatly suppressed.

[0142] On comparing the binomial approximation method, trinomialapproximation method, and polynomial correction method with J=5 and withJ=10, it is seen that by increasing the number of terms in the pileupcorrection, the precision of the calculated energy value obtained isimproved.

[0143]FIGS. 15A and 15B are graphs showing the distribution of energyvalues for input signal pulses, using (A) the trinomial approximationmethod, and (B) the polynomial approximation method with J=5.

[0144]FIGS. 15A and 15B show energy distributions obtained insimulations conducted under five conditions for the input count rate:(1) 0.01 Mcps, (2) 1 Mcps, (3) 2 Mcps, (4) 3 Mcps, and (5) 4 Mcsp. Asthe input count rate increases, the energy resolution declines somewhat,and the center value of the energy distribution is shifted somewhattoward higher energies; but it is seen that pileup correction greatlysuppresses the energy shift and decline in energy resolution.

[0145] As explained above, when applying the binomial approximationmethod, trinomial approximation method, and polynomial correction methodto a general waveform, by increasing the number of terms in the pileupcorrection (the number of signal pulses used in pileup correction), theprecision of the calculated energy value is improved. On the other hand,if the number of terms in pileup correction becomes large, thecomputations needed to calculate the energy become complex, and whenusing lookup tables, the number of lookup tables needed and the numberof data values increase. Consequently it is preferable that anappropriate number of terms for pileup correction, and an appropriatecorrection method, be selected according to the required precision ofthe calculated energy values and the anticipated frequency of signalpulse input.

[0146] In energy measurements, sometimes data values for the acquiredintegrated signal intensity Q and pulse interval T for continuouslyinput signal pulses P are collected in list mode, and energycalculations are performed in off-line analysis after data collection,or in parallel with data collection. In such cases, it is possible toexecute computations for energy calculations in software separate fromthe data collection; hence application is also possible for complexcomputations, as in the case of the polynomial correction method forpileup correction in which the number of terms J is increased.

[0147] As the configuration of an apparatus for energy calculationsperformed in off-line analysis, an energy calculation apparatusconfiguration is possible in which, of the above-described configurationof the energy measurement apparatus 1, the energy calculation unit 10 isprovided separately (for example, as a computer having software forenergy calculation). In this case, in place of the energy calculationunit 10 in the energy measurement apparatus 1, recording means whichrecords integrated signal intensities Q, pulse intervals T and otherdata on prescribed recording media may be provided.

[0148] In energy measurements of general waveforms other than singleexponential function waveforms, a configuration may be employed whichperforms signal processing after shaping of the pulse waveform, as forexample by using a differentiation circuit or other waveform-shapingcircuit to first eliminate components with a long attenuation timeconstant.

[0149] It was previously noted that when expressing an emission pulsewaveform by a single exponential function, the Wong method may be usedas a conventional method. In order to compare the results of thesemethods, the single exponential function correction method of thisinvention, and the above Wong method, were used to conduct simulationsof energy calculations and pileup correction. Here, the pulse waveformof signal pulses P was assumed to be a time domain waveform having asingle exponential function component with an attenuation time constantτ of 300 ns; the energy, expressed as a number of photoelectrons, was2000. Also, in the Wong method, in order to reduce the effect of thenoise signal contained in the current signal, it was assumed that signalpulse smoothing was performed by a smoothing circuit prior to signalprocessing; simulations were conducted under three conditions, withsmoothing times of 10 ns (conventional 1), 20 ns (conventional 2), and50 ns (conventional 3).

[0150]FIG. 16 is a graph showing the FWHM of energy values calculatedfor input signal pulses using the single exponential function correctionmethod, and the Wong method, which is a conventional correction method.From these graphs it is seen that the effect in suppressing reductionsin energy resolution accompanying increases in the input count rate isgreater for the single exponential function correction method than whenusing the Wong method with signal pulse smoothing.

[0151]FIG. 17A and FIG. 17B are graphs showing the distribution ofenergy values calculated for input signal pulses using (A) the singleexponential function correction method, and (B) the Wong method.

[0152] The energy distributions shown in FIGS. 17A and 17B were obtainedin simulations conducted under four conditions for the input count rate:(1) 0.01 Mcps, (2) 1 Mcps, (3) 2.5 Mcps, and (4) 5 Mcps. From thesegraphs also, it is seen that the effect in suppressing reductions inenergy resolution accompanying increases in the input count rate isgreater for the single exponential function correction method.

[0153] Next, the case in which pulse shape discrimination is used isexplained, as a fourth embodiment of an energy measurement apparatus ofthis invention. In pulse shape discrimination (PSD), a plurality ofscintillators having different emission attenuation time constants aremounted on a photomultiplier tube, and detection is performed bydiscriminating the scintillator detecting radiation based on differencesin the signal waveform. For example, if a scintillator for γ-rays and ascintillator for neutrons are mounted onto a single photomultiplier tubeand employed in pulse shape discrimination, γ rays and neutron rays canbe simultaneously discriminated and measured. Also, some scintillatorsexhibit different emission attenuation time constants depending on thetype of radiation detected, whether γ rays, α particles, heavy particlebeams, or similar. When using such a scintillator, pulse shapediscrimination can be used to discriminate and measure differentradiation types. There are various specific pulse shape discriminationmethods. In the example below, a pulse shape discrimination method isemployed which utilizes the fact that the ratio of integration valuesobtained when a signal pulse is integrated over two different times isdifferent depending on the emission attenuation time constant; but thisembodiment is not limited to this method.

[0154]FIG. 18 is a block diagram showing the configuration of the fourthembodiment, using such a pulse shape discrimination method. The energymeasurement apparatus 1 has a configuration which can be applied tomeasurement of the energy of signal pulses when two kinds of signalpulses P for measurement are input, both having a single exponentialfunction waveform, with different attenuation time constants τ¹, τ₂.

[0155] The configuration of the energy measurement apparatus 1 of thisembodiment is similar to the embodiment shown in FIG. 3 with respect tothe trigger signal generator 21, gate signal generator 22, delay circuit31, and gate integrator 32.

[0156] In this embodiment, in place of the pulse interval measurementunit 23, a sample time setting unit 24 is provided, which functions asmeans for pulse interval measurement. The sample time setting unit 24measures the pulse interval T₀ of the signal pulse P₀, and in additionsets the effective integration time T′ (cf. eq. (7)) which is the sampletime for integrating the signal intensity, based on the measured pulseinterval T₀, and indicates this effective integration time T′ to thegate signal generator 22. Based on the trigger signal input from thetrigger signal generator 21 and the effective integration time T′indicated by the sample time setting unit 24, the gate signal generator22 generates a gate signal to indicate integration of the signalintensity.

[0157] Based on the gate signal indication, the gate integrator 32integrates the signal intensity of the signal pulse P₀ input from thedelay circuit 31. The integrated signal intensity obtained byintegration at the effective integration time T′ indicated by the gatesignal is output as integrated signal intensity data Q₀ via an A/Dconverter 33 comprising a sample hold circuit and ADC.

[0158] On the other hand, separately from the effective integration timeT′ which is set for each signal pulse P₀, an integration time T_(P) isindicated to the gate integrator 32. This integration time T_(P) is setto a fixed value in advance, to a time shorter than the anticipatedeffective integration time T′ (T′>T_(P)). The integrated signalintensity obtained by integration at the integration time T_(P) isoutput as integrated signal intensity data Q_(P) via an A/D converter 34comprising a sample hold circuit and ADC.

[0159] The integrated signal intensity Q₀ output from the A/D converter33 and the integrated signal intensity Q_(P) output from the A/Dconverter 34 are input to the pulse shape discriminator 25. The pulseshape discriminator 25 uses the ratio Q₀/Q_(P) of the integrated signalintensities Q₀ and Q_(P) with different integration times to performdiscrimination of a plurality of pulse shape types (in this case, twotypes) based on shape discrimination conditions set in advance, andoutputs the result x₀ of shape discrimination thus obtained (x₀=1 or 2).

[0160] The energy calculation unit 10 has an energy computing unit 11,lookup table 12, and two buffer memories 46, 47. The energy computingunit 11 performs computations necessary to calculate the energy E₀ of aninput signal pulse P₀ to be measured. The lookup table 12 storescoefficient data used in computations executed by the energy computingunit 11.

[0161] For a signal pulse P₀ to be measured at each moment, theintegrated signal intensity Q₀ output from the A/D converter 33, thepulse interval T₀ output from the sample time setting unit 24, and theshape discrimination result x₀ output from the pulse shape discriminator25 are each input to the energy computing unit 11, and are stored in thebuffer memory 46. Also, the integrated signal intensity Q₁, pulseinterval T₁ and shape discrimination result x₁ for the signal pulse P₁preceding the signal pulse P₀ are stored in the buffer memory 47. Thesedata values become input data for computations by the energy computingunit 11 to calculate the energy.

[0162] The method of calculation of the energy E with pulse shapediscrimination is explained in detail below, referring to theconfiguration of the energy measurement apparatus 1 shown in FIG. 18.

[0163] Suppose that, in the signal pulses P input to the energymeasurement apparatus 1 for measurement, there exist two kinds of signalpulses, having pulse waveforms with different attenuation time constantsτ₁ and τ₂. Then the pulse waveform f_(k)(t), integrated signal intensityQ_(k)(T), and integration response G_(k)(T) for a signal pulse withattenuation time constant τ_(k)(k=1 or 2) are, respectively,

f _(k)(t)=(E/τ _(k))exp(−t/τ _(k)) (k=1or 2)  (16a)

Q _(k)(T)=∫₀ ^(T) f _(k)(t)dt=E{1−exp(−T/τ _(k))}  (16b)

G _(k)(T)=1−exp(−T/τ _(k)).  (16c)

[0164] Of the two integration times, if the longer effective integrationtime T′ is set according to eq. (7) using the reset time T_(r) andmaximum integration time T_(max), then the effective integrationresponse H_(k)(T) can be written

H _(k)(T)=G _(k)(T′)=1−exp(−T′/τ _(k)).  (17)

[0165] The shorter integration time T_(P) is set and fixed in advance,as described above.

[0166] As shown in FIG. 18, suppose that the shape discriminationresults for the signal pulse P₀ to be measured and the preceding signalpulse P₁ are k=x₀, x₁ (both either 1 or 2), respectively. Then theenergy E₀ after pileup correction for the signal pulse P₀ can becalculated using the following eq. (18): $\begin{matrix}{\begin{matrix}{E_{0} = {\frac{Q_{0}}{H_{x0}\left( T_{0} \right)} - {Q_{1}\frac{\exp \left( {{- T_{1}}/\tau_{x1}} \right)}{H_{x1}\left( T_{1} \right)}}}} \\{= {{Q_{0} \cdot {A_{x0}\left( T_{0} \right)}} - {Q_{1} \cdot {{B_{x1}\left( T_{1} \right)}.}}}}\end{matrix}\quad} & (18)\end{matrix}$

[0167] The coefficients A₁(T), B₁(T) for pulse waveforms withattenuation time constant τ₁, and the coefficients A₂(T), B₂(T) forpulse waveforms with attenuation time constant τ₂, can be computed bythe energy computing unit 11 on each occasion. Or, computations can beperformed in advance to determine the coefficients A₁(T), B₁(T), A₂(T),B₂(T), and a lookup table 12 created. In this case, it is necessary toprepare the lookup tables with twice the number of tables and the datavolume, compared with the case in which pulse shape discrimination isnot performed.

[0168] Here, the pulse shape discrimination performed by the pulse shapediscriminator 25 to discriminate the two types of pulse shapes withattenuation time constants τ₁, τ₂ is explained.

[0169]FIG. 19A and FIG. 19B are graphs showing the integration timesettings for performing pulse shape discrimination of signal pulses P.Here, the graph of FIG. 19A shows a signal waveform the signal intensityof which changes with time; the graph of FIG. 19B shows the integratedwaveform, which is an integrated signal intensity changing with time,obtained by integrating the signal waveform shown in FIG. 19A.

[0170] In the energy measurement apparatus 1 of this embodiment, asshown in FIGS. 19A and 19B, two integration times T₀′ and T_(P) are setfor integration of the signal intensity of the signal pulse P₀. Ofthese, the longer integration time T₀′ is the ordinary effectiveintegration time, similar to the case in which pulse shapediscrimination is not performed, shown in FIGS. 5A and 5B. The shorterintegration time T_(P) is an integration time which is set and fixed forthe purpose of pulse shape discrimination. In the pulse shapediscriminator 25, by comparing the integrated signal intensity Q₀obtained using the longer integration time T′ and the integrated signalintensity Q_(P) obtained using the shorter integration time T_(P), thetwo types of pulse shape can be discriminated.

[0171]FIG. 20 is a graph showing the method of discrimination of thepulse shapes of signal pulses. In this graph, the horizontal axisindicates the effective integration time T′, which fluctuates dependingon the pulse interval T for each signal pulse P, and the vertical axisindicates the ratio Q₀/Q_(P) of integrated signal intensities.

[0172] Due to the difference in the rates of attenuation of pulse shapeswith attenuation time constant τ₁ and pulse shapes with attenuation timeconstant τ₂, even when the integration time T′ (T′>T_(P)) is the same,the ratio R(T′)=Q₀/Q_(P) of the integrated signal intensities Q₀ andQ_(P) will have different values for the two pulse shapes. Hence byusing the value of this ratio, the two types of pulse shape can bediscriminated.

[0173] The graph of FIG. 20 shows the dependences on the effectiveintegration time T′ of the ratio R₁(T′)=G₁(T′)/G₁(T_(P)) of integratedsignal intensities for the pulse shape with attenuation time constantτ₁, and the ratio R₂(T′)=G₂(T′)/G₂(T_(P)) of integrated signalintensities for the pulse shape with attenuation time constant τ₂.

[0174] If the integration time is T′=T_(P), then these ratios areR₁(T′)=R₂(T′)=1. As the effective integration time T′ lengthens, theratios R₁(T′) and R₂(T′) both tend to increase, and at the same time thedifference between them increases. Hence the minimum integration timeT_(min) for an effective integration time T′ is set to an integrationtime enabling differentiation by the pulse shape discriminator 25 of thedifference between the ratios R₁(T′) and R₂(T′). Also, the shapediscriminator curve R_(P)(T′) is set substantively in the center of thetwo curves for the ratios R₁(T′) and R₂(T′).

[0175] Thus by comparing the value of the above shape discriminationcurve R_(P)(T′) in the pulse shape discriminator 25 with the ratioR(T′)=Q₀/Q_(P) of integrated signal intensities actually obtained for asignal pulse P₀, pulse shapes can be discriminated.

[0176] In other words, if the ratio obtained is Q₀/Q_(P)>R_(P), then thesignal pulse P₀ for measurement has a pulse shape with attenuation timeconstant τ₁. At this time, the pulse shape discriminator 25 outputs x₀=1as the shape discrimination result. On the other hand, ifQ₀/Q_(P)<R_(P), then the signal pulse P₀ has a pulse shape withattenuation time constant τ₂. At this time, the pulse shapediscriminator 25 outputs x₀=2 as the shape discrimination result.

[0177] In this way, by performing energy measurements accompanied bypulse shape discrimination, it is possible to perform energycalculations using a calculation method appropriate to different pulseshapes when signal pulses with different pulse shapes are input, as forexample when signal pulses from a plurality of scintillators havingdifferent attenuation time constants are input for energy measurement.

[0178] Simulations were performed of energy calculations and pileupcorrection for the above case with pulse shape discrimination. It wasassumed that there are two types of time domain waveform as the pulseshapes of signal pulses P, expressed as single exponential functioncomponents having respective attenuation time constants τ₁=100 ns andτ₂=50 ns, and it was further assumed that these pulses are generatedrandomly with the same probability. The energy was assumed to beconstant (2000 photoelectrons). As other conditions, the reset timeT_(r) was set to 50 ns, the fixed integration time T_(P) to 30 ns, theminimum integration time for an effective integration time T′ toT_(min)=50 ns, and the maximum integration time to T_(max)=500 ns.

[0179]FIG. 21A to FIG. 21C are graphs showing the distribution of energyvalues calculated for input signal pulses using pulse shapediscrimination and pileup correction. FIG. 21A shows the energydistribution for condition 1, in which integration time correction andpileup correction were not performed; FIG. 21B shows the energydistribution for condition 2, in which integration time correction onlywas performed; and FIG. 21C shows the energy distribution for condition3, in which integration time correction and pileup correction were bothperformed.

[0180] Each of the graphs shows the energy distributions obtained insimulations under four different conditions for the input count rate:(1) 0.1 Mcps, (2) 1 Mcps, (3) 2.5 Mcps, and (4) 5 Mcps.

[0181] In the graph of FIG. 21A, which shows the integrated signalintensity Q as the energy E without modification, and without performingeither pileup correction or integration time correction, the energyresolution declines as the input count rate increases; also, there occura distribution at low energies as the integration time becomes shorter,and a distribution at high energies due to signal pulse pileup. In thegraph of FIG. 21B, in which only integration time correction wasperformed, the low-energy distribution due to the integration time hasvanished, but the high-energy distribution due to pileups remains.

[0182] On the other hand, in the graph of FIG. 21C resulting when bothintegration time correction and pileup correction are performed, boththe distributions on the low energy and on the high energy sides havevanished. Also, the energy resolution is improved.

[0183]FIG. 22 is a graph showing the FWHM and FWTM of energy valuescalculated for input signal pulses using pulse shape discrimination andpileup correction. Similarly to FIGS. 21A through 21C, curvescorresponding to each of the conditions 1, 2 and 3 are shown. From thisgraph, it is seen that reduction of the energy resolution accompanyingan increase in the number of input signal pulses is greatly suppressedunder condition 3, in which both integration time correction and pileupcorrection are performed.

[0184]FIG. 23 is a graph showing the count rate characteristic for theabove simulation results. As a result of setting the minimum integrationtime to 50 ns, the output count rate reaches saturation at 10 Mcps.

[0185] Next, as a fifth embodiment of an energy measurement apparatus,the case of application to signal pulses from a two-dimensional positiondetection-type radiation detector, used in gamma cameras, PET systemsand similar, is explained. As one example, the case of application tosignal pulses from a two-dimensional position detection-type blockdetector, commonly used in PET systems, is described. FIG. 24 is a blockdiagram showing the configuration of such an embodiment. As shown inFIG. 25, in the block detector used here, scintillator SC crystals ofBGO (bismuth germanium oxide) or similar are arranged in atwo-dimensional matrix (for example, an 8-row by 8-column matrix), andconnected optically to four square-shape photomultiplier tubes PMT; ifthe signal pulses from the four photomultiplier tubes PMT are P_(A),P_(B), P_(C), P_(D), the energies of the respective signal pulses areE_(A), E_(B), E_(C), E_(D), and the sum of these energies is E, then theX and Y coordinates of a scintillator detecting a γ ray can bedetermined from $\begin{matrix}{{X = \frac{\left( {E_{A} + E_{B}} \right) - \left( {E_{C} + E_{D}} \right)}{E}},{Y = {\frac{\left( {E_{A} + E_{C}} \right) - \left( {E_{B} + E_{D}} \right)}{E}.}}} & (19)\end{matrix}$

[0186] In place of the four photomultiplier tubes, a single positiondetection-type photomultiplier tube may be used.

[0187] When pileup of signal pulses occurs in such an apparatus, notonly is the energy of radiation not correctly measured, but theradiation detection position is not correctly measured, so thatdegradation of the image resolution and image distortion occur.

[0188] The configuration of the energy measurement apparatus 1 of thisembodiment is, in essence, a modification of the configuration shown inFIG. 4. Specifically, the trigger signal generator 21, gate signalgenerator 22, and pulse interval measurement unit 23 are similar to theembodiment shown in FIG. 4.

[0189] Also, an addition circuit 35 is provided which generates a signalpulse P₀ which is the sum obtained by adding the four signal pulsesP_(A0), P_(B0), P_(C0), P_(D0) input for measurement. The signal pulseP₀ generated by this addition circuit 35 is input to the trigger signalgenerator 21.

[0190] In place of the delay circuit 31 and gate integrator 32, delaycircuits 31 _(A), 31 _(B), 31 _(C), 31 _(D), and 31 _(F), as well asgate integrators 32 _(A), 32 _(B), 32 _(C), 32 _(D), 32 _(E),corresponding to the five signal pulses P_(A0), P_(B0), P_(C0), P_(D0),P₀ are provided.

[0191] Also, in place of the buffer memories 40 and 41 in the energycalculation unit 10, the buffer memories 40 _(A), 40 _(B), 40 _(C), 40_(D), 40 _(E), storing the integrated signal intensities Q_(A0), Q_(B0),Q_(C0), Q_(D0), Q₀ corresponding to the signal pulses P_(A0), P_(B0),P_(C0), P_(D0), P₀ respectively, and the buffer memories 41 _(A), 41_(B), 41 _(C), 41 _(D), 41 _(E), storing the integrated signalintensities Q_(A1), Q_(B1), Q_(C1), Q_(D1), Q₁ corresponding to thesignal pulses P_(A1), P_(B1), P_(C1), P_(D1), P₁ respectively, areprovided. Also, a buffer memory 40 _(T) storing the pulse interval T₀corresponding to the signal pulse P₀, and a buffer memory 41 _(T)storing the pulse interval T₁ corresponding to the signal pulse P₁, areprovided.

[0192] Also, in place of the energy computing unit 11, the energycomputing units 11 _(A), 11 _(B), 11 _(C), 11 _(D), 11 _(E)corresponding to the signal pulses P_(A0), P_(B0), P_(C0), P_(D0), P₀respectively are provided. In FIG. 24, the lookup table 12 provided inthe energy calculation unit 10 is omitted.

[0193] In the above configuration, the signal pulse P_(A0) is subjectedto signal processing by the delay circuit 31 _(A), gate integrator 32_(A), buffer memories 40 _(A) and 41 _(A), and energy computing unit 11_(A), and the corresponding energy E_(A0) is calculated. The signalpulse P_(B0) is subjected to signal processing by the delay circuit 31_(B), gate integrator 32 _(B), buffer memories 40 _(B) and 41 _(B), andenergy computing unit 11 _(B), and the corresponding energy E_(B0) iscalculated. The signal pulse P_(C0) is subjected to signal processing bythe delay circuit 31 _(C), gate integrator 32 _(C), buffer memories 40_(C) and 41 _(C), and energy computing unit 11 _(C), and thecorresponding energy E_(C0) is calculated. And, the signal pulse P_(D0)is subjected to signal processing by the delay circuit 31 _(D), gateintegrator 32 _(D), buffer memories 40 _(D) and 41 _(D), and energycomputing unit 11 _(D) and the corresponding energy E_(D0) iscalculated.

[0194] The signal pulse P₀, obtained by adding the signal pulses P_(A0),P_(B0), P_(C0), P_(D0), is subjected to signal processing by the delaycircuit 31 _(E), gate integrator 32 _(E), buffer memories 40 _(E), 41_(E), and energy computing unit 11 _(E), and the corresponding totalenergy E₀ is calculated. From these energies E_(A0), E_(B0), E_(C0),E_(D0), E₀, the position of the scintillator detecting the γ ray can bedetermined using eq. (19).

[0195] However, the X and Y coordinates obtained in this way are notnecessarily proportional to the accurate X and Y coordinates of thescintillator, and in addition contain statistical noise. On the otherhand, it is known that the accurate position of the scintillator is oneof a plurality of positions in the matrix, and so a lookup tableprepared in advance must be used to convert measured coordinate valuesinto correct coordinate values. Also, the energy E₀ corresponds to thedetected radiation energy, and so by performing pulse height analysis ofthis signal, the radiation energy can be selected.

[0196] The method and apparatus for energy measurement of this inventionare not limited to the above-described embodiments, and variousmodifications are possible. For example, the signal pulse pileupcorrection method is not limited to the above-described singleexponential function correction method, binomial approximation method,trinomial approximation method, or polynomial correction method, andvarious correction methods which employ the integrated signal intensity,pulse interval, and energy may be used, according to the details of thepulse waveform and other factors.

[0197] Also, it is preferable that the configuration of the buffermemories provided in the energy calculation unit 10 be modifiedappropriately according to the data to be used in pileup correction.

[0198] As has been explained in detail above, the method and apparatusfor energy measurement of this invention can be used as an energymeasurement method and apparatus capable of the correct and precisemeasurement of the energies of individual signal pulses, even at highcount rates. That is, by means of an energy measurement method andapparatus which calculate energy from the integrated signal intensityand pulse interval of the signal pulse for measurement, and in additionperform pileup correction using the integrated signal intensity or theenergy, or both, and the pulse interval of signal pulses input beforethe signal pulse to be measured, the effect of other signal pulsespiled-up with the signal pulse is eliminated, so that correct andprecise measurement of the energies of individual signal pulses ispossible.

[0199] Such problems of signal pulse pileup occur in various types ofradiation detector and in other devices. Hence the above-describedmethod and apparatus for energy measurement can be applied to variousdevices and systems in which measurement of information relating toradiation energies and radiation detection positions is necessary, suchas for example scintillation detectors, energy spectrometers, radiationposition detectors, gamma cameras, SPECT systems, and PET systems, andcan ensure that the energy resolution and image resolution of suchsystems and devices remain satisfactory even at high count rates.

What is claimed is:
 1. An energy measurement method, in which the signalintensity of the pulse waveform of a signal pulse for measurement isintegrated and the energy of said signal pulse is measured, comprising:a pulse interval acquisition step, in which the pulse interval of theinputted signal pulse, which is the time interval from said signal pulseto the next signal pulse, is acquired; an integrated intensityacquisition step, in which the signal intensity of said signal pulse isintegrated over a prescribed integration time set so as to correspond tosaid pulse interval, to acquire the integrated signal intensity; and, anenergy calculation step, in which the energy corresponding to the totalintegrated intensity of said signal pulse is calculated from saidintegrated signal intensity acquired in said integrated intensityacquisition step, and from said pulse interval acquired in said pulseinterval acquisition step; and wherein in said energy calculation step,pileup correction of the uncorrected energy calculated from saidintegrated signal intensity and said pulse interval for said signalpulse to be measured is performed, using at least one of said integratedsignal intensity or said energy, and said pulse interval, for the signalpulse inputted prior to the signal pulse for measurement to calculatesaid corrected energy.
 2. The energy measurement method according toclaim 1 wherein, in said energy calculation step, coefficients A(T) andB(T), which are determined based on said pulse interval T, are used tocalculate said energy E₀ of the signal pulse P₀ inputted at time to fromthe integrated signal intensity Q₀ and pulse interval T₀ of said signalpulse P₀, and from the integrated signal intensity Q₁ and pulse intervalT₁ of the signal pulse P₁ inputted in succession at time t₁ (t₁<t₀),according to the equation E ₀ =Q ₀ ·A(T ₀)−Q ₁ ·B(T ₁).
 3. The energymeasurement method according to claim 1 wherein, in said energycalculation step, the number of signal pulses used in said pileupcorrection, from among the signal pulses inputted prior to said signalpulse for measurement, is set as J (where J is an integer greater thanor equal to 1), and coefficients C₀(T) and C_(j)(T) (j=1, . . . , J),which are determined based on said pulse interval T, are used tocalculate said energy E₀ of the signal pulse P₀ inputted at time t₀ fromthe integrated signal intensity Q₀ and pulse interval T₀ of said signalpulse P₀, and from the energies E_(j) and pulse intervals T_(J) of the Jsignal pulses P_(J) inputted in succession at times t_(j)(t_(j)<t_(j−1)), according to the equation$E_{0} = {{Q_{0} \cdot {C_{0}\left( T_{0} \right)}} - {\sum\limits_{j = 1}^{J}{E_{j} \cdot {{C_{j}\left( T_{j} \right)}.}}}}$


4. The energy measurement method according to claim 1 wherein, in saidenergy calculation step, coefficients D₀(T), D₁(T) and D₂(T), which aredetermined based on said pulse interval T, are used to calculate saidenergy E₀ of the signal pulse P₀ inputted at time t₀, from theintegrated signal intensity Q₀ and pulse interval T₀ of said signalpulse P₀, from the energy E₁ and pulse interval T₁ of the signal pulseP₁ inputted in succession at time t₁ (t₁<t₀), and from the integratedsignal intensity Q₂ and pulse interval T₂ of the signal pulse P₂inputted in succession at time t₂ (t₂<t₁), according to the equation E ₀=Q ₀ ·D ₀(T ₀)−E ₁ ·D ₁(T ₁)−Q ₂ ·D ₂(T ₂).
 5. The energy measurementmethod according to claim 2, wherein a lookup table, created from thevalues of said coefficients which are determined in advance for aplurality of said pulse interval values, is used in said energycalculation step for each of said coefficients used in calculating saidenergy and determined based on said pulse interval T.
 6. The energymeasurement method according to claim 3, wherein a lookup table, createdfrom the values of said coefficients which are determined in advance fora plurality of said pulse interval values, is used in said energycalculation step for each of said coefficients used in calculating saidenergy and determined based on said pulse interval T.
 7. The energymeasurement method according to claim 4, wherein a lookup table, createdfrom the values of said coefficients which are determined in advance fora plurality of said pulse interval values, is used in said energycalculation step for each of said coefficients used in calculating saidenergy and determined based on said pulse interval T.
 8. The energymeasurement method according to claim 1, further comprising a pulseshape discrimination step in which the pulse shape of said signal pulseis discriminated among a plurality of pulse shape types, based on shapediscrimination conditions set in advance; and wherein, in said energycalculation step, said energy is calculated using a calculation methodcorresponding to the type of said pulse shape discriminated in saidpulse shape discrimination step.
 9. An energy measurement apparatuswhich integrates the signal intensity of the pulse waveform of a signalpulse for measurement to measure the energy of said signal pulse,comprising: trigger signal generation means, which accepts as input oneof the branched signal pulses of the inputted signal pulse and generatesa trigger signal corresponding to said signal pulse; gate signalgeneration means, which accepts as input said trigger signal from saidtrigger signal generation means, and based on said trigger signal,generates a gate signal to indicate integration of the signal intensity;pulse interval measurement means, which accepts as input said triggersignal from said trigger signal generation means, and measures the timeinterval from said trigger signal until the next trigger signal as thepulse interval of said signal pulse; delay means, which accepts as inputthe other of said inputted branched signal pulses, and delays saidsignal pulse by a prescribed delay time; gate integration means, whichaccepts as input said signal pulse delayed by said delay means and saidgate signal from said gate signal generation means, and integrates thesignal intensity of said signal pulse for a prescribed integration timewhich is set based on the indication of said gate signal, to acquire theintegrated signal intensity; and, energy calculation means, whichcalculates the energy corresponding to the total integrated intensity ofsaid signal pulse from said integrated signal intensity acquired by saidgate integration means and from said pulse interval measured by saidpulse interval measurement means; and wherein said energy calculationmeans performs pileup correction of the uncorrected energy calculatedfrom said integrated signal intensity and said pulse interval of saidsignal pulse for measurement, using at least one of said integratedsignal intensity or said energy, and said pulse interval, of the signalpulse inputted prior to the signal pulse for measurement to calculatesaid corrected energy.
 10. The energy measurement apparatus according toclaim 9, wherein said energy calculation means has energy computingmeans which performs computations to calculate said energy, includingcomputations for said pileup correction; a first buffer memory, whichstores said integrated signal intensity and said pulse interval for saidsignal pulse for measurement; and a second buffer memory, which storesat least one of said integrated signal intensity or said energy, andsaid pulse interval, for the signal pulse inputted prior to the signalpulse for measurement.
 11. The energy measurement apparatus according toclaim 9, wherein said energy calculation means uses coefficients A(T)and B(T), determined based on said pulse interval T, to calculate saidenergy E₀ of the signal pulse P₀ inputted at time to from the integratedsignal intensity Q₀ and pulse interval T₀ of said signal pulse P₀, andfrom the integrated signal intensity Q₁ and pulse interval T₁ of thesignal pulse P₁ inputted in succession at time t₁ (t₁<t₀), according tothe equation E ₀ =Q ₀ ·A(T ₀)−Q ₁ ·B(T ₁).
 12. The energy measurementapparatus according to claim 9, wherein said energy calculation meanssets J (where is an integer greater than or equal to 1) as the number ofsignal pulses, from among the signal pulses inputted prior to saidsignal pulse for measurement, for use in said pileup correction, anduses the coefficients C₀(T) and C_(J)(T) (j=1, . . . , J), determinedbased on said pulse interval T, to calculate said energy E₀ of thesignal pulse P₀ inputted at time to from the integrated signal intensityQ₀ and pulse interval T₀ of said signal pulse P₀, and from the energiesE_(j) and pulse intervals T_(j) of the J signal pulses P_(j) inputted insuccession at times t_(j) (t_(j)<t_(j−1)), according to the equation$E_{0} = {{Q_{0} \cdot {C_{0}\left( T_{0} \right)}} - {\sum\limits_{j = 1}^{J}{E_{j} \cdot {{C_{j}\left( T_{j} \right)}.}}}}$


13. The energy measurement apparatus according to claim 9, wherein saidenergy calculation means uses coefficients D₀(T), D₁(T) and D₂(T),determined based on said pulse interval T, to calculate said energy E₀of the signal pulse P₀ inputted at time t₀, from the integrated signalintensity Q₀ and pulse interval T₀ of said signal pulse P₀, from theenergy E₁ and pulse interval T₁ of the signal pulse P₁ inputted insuccession at time t₁ (t₁<t₀), and from the integrated signal intensityQ₂ and pulse interval T₂ of the signal pulse P₂ inputted in successionat time t₂ (t₂<t₁), according to the equation E ₀ =Q ₀ ·D ₀(T ₀)−E ₁ ·D₁(T ₁)−Q ₂ ·D ₂(T ₂).
 14. The energy measurement apparatus according toclaim 11, wherein said energy calculation means has a lookup table foreach of said coefficients used in calculating said energy and determinedbased on said pulse interval T, said lookup tables being created fromthe values of said coefficients which are determined in advance for aplurality of said pulse interval values.
 15. The energy measurementapparatus according to claim 12, wherein said energy calculation meanshas a lookup table for each of said coefficients used in calculatingsaid energy and determined based on said pulse interval T, said lookuptables being created from the values of said coefficients which aredetermined in advance for a plurality of said pulse interval values. 16.The energy measurement apparatus according to claim 13, wherein saidenergy calculation means has a lookup table for each of saidcoefficients used in calculating said energy and determined based onsaid pulse interval T, said lookup tables being created from the valuesof said coefficients which are determined in advance for a plurality ofsaid pulse interval values.
 17. The energy measurement apparatusaccording to claim 9, further comprising pulse shape discriminationmeans which discriminates the pulse shape of said signal pulse among aplurality of types of pulse shapes based on shape discriminationconditions set in advance; and wherein said energy calculation meanscalculates said energy using a calculation method corresponding to thetype of said pulse shape, discriminated by said pulse shapediscrimination means.
 18. The energy measurement apparatus according toclaim 9, wherein said integration time over which the signal intensityof said signal pulse is integrated in said gate integration means isset, for each of said signal pulses for measurement, as an effectiveintegration time T′, which is the shorter time among a maximumintegration time T_(max), set in advance, and the times T−T_(r) obtainedby subtracting the reset time T_(r) of said gate integration means fromsaid pulse interval T, such that: T′=min(T _(max) , T−T _(r)).